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Simplifying 2x2 + -12x = 151 Reorder the terms: -12x + 2x2 = 151 Solving -12x + 2x2 = 151 Solving for variable 'x'. Reorder the terms: -151 + -12x + 2x2 = 151 + -151 Combine like terms: 151 + -151 = 0 -151 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -75.5 + -6x + x2 = 0 Move the constant term to the right: Add '75.5' to each side of the equation. -75.5 + -6x + 75.5 + x2 = 0 + 75.5 Reorder the terms: -75.5 + 75.5 + -6x + x2 = 0 + 75.5 Combine like terms: -75.5 + 75.5 = 0.0 0.0 + -6x + x2 = 0 + 75.5 -6x + x2 = 0 + 75.5 Combine like terms: 0 + 75.5 = 75.5 -6x + x2 = 75.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 75.5 + 9 Reorder the terms: 9 + -6x + x2 = 75.5 + 9 Combine like terms: 75.5 + 9 = 84.5 9 + -6x + x2 = 84.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 84.5 Calculate the square root of the right side: 9.192388155 Break this problem into two subproblems by setting (x + -3) equal to 9.192388155 and -9.192388155.Subproblem 1
x + -3 = 9.192388155 Simplifying x + -3 = 9.192388155 Reorder the terms: -3 + x = 9.192388155 Solving -3 + x = 9.192388155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 9.192388155 + 3 Combine like terms: -3 + 3 = 0 0 + x = 9.192388155 + 3 x = 9.192388155 + 3 Combine like terms: 9.192388155 + 3 = 12.192388155 x = 12.192388155 Simplifying x = 12.192388155Subproblem 2
x + -3 = -9.192388155 Simplifying x + -3 = -9.192388155 Reorder the terms: -3 + x = -9.192388155 Solving -3 + x = -9.192388155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -9.192388155 + 3 Combine like terms: -3 + 3 = 0 0 + x = -9.192388155 + 3 x = -9.192388155 + 3 Combine like terms: -9.192388155 + 3 = -6.192388155 x = -6.192388155 Simplifying x = -6.192388155Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.192388155, -6.192388155}
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